REFERENCE TO RELATED APPLICATIONS

This application claims priority to PCT/US2018/022948, filed March 16, 2018, PCT/US2018/048519, filed August 29, 2018 and PCT/US2018/054374, filed October 4, 2018, the entire content of each application is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to a method and a printing system for printing on a top surface of three-dimensional objects, in particular on a top surface of cylindrical objects, and in particular relates to a method and a printing system to compensate image distortion occurring in inkjet printing on flat surfaces during direct to shape printing.

BACKGROUND OF THE INVENTION

As in every other production industry, branding of products is a pivotal strategic and marketing factor for the producers of bottled beverages. When aiming at developing a unique branding for bottled beverages with a largely uniform container design, such as wine bottles with screw caps, the design of the label and the screw cap are essentially the only designable components. For that reason, there is a need for printing facilities that enable printing on labels and screw caps. The geometry of the screw caps poses a particular challenge for a corresponding printing apparatus, since screw caps are cylindrical objects with a planar top surface and a cylindrical lateral surface, both of which have to be printed. Such a printing process requires - by far - more advanced technologies than printing on planar labels, for which conventional paper printing technology may be applied.

An exemplary apparatus for printing on cylindrical objects is disclosed by WO 2015/16628 Al. It comprises a plurality of stationary printheads and a holding device for holding the cylindrical objects in a fixed orientation. The holding device moves the cylindrical objects into the vicinity of the printheads such that the printheads may print on the cylindrical object. The fixed orientation of the cylindrical objects ensures a reproducible orientation of the printheads relative to the cylindrical objects, which allows for simplifying the ink feed system needed to feed the ejectors of the printheads. The conventional printing apparatus for cylindrical objects mentioned above is designed to print on the lateral surface of the cylindrical objects. However, for cylindrical objects, such as screw caps, it is desirable to allow printing on the top surface of the cylindrical objects as well.

In this regard, it is known to print three-dimensional objects and parts of it surface or its entire surface via direct to shape printing (DTS). In commonly known DTS printing systems, the nozzle plate of digital inkjet printheads has to be formed flat. In addition, the maximum operation distance of the digital inkjet printheads to the subject to be printed on is limited to a few millimeters. Thus, DTS has to be performed in several steps when printing on three-dimensional objects.

In case of printing on a lateral surface and a top surface of a cylindrical object via DTS, in a first step, the lateral surface is being printed via a printhead. Afterwards, the object is tilted such that the top surface is facing the printhead. Then, in a further step, the top surface is translated in a linear movement underneath the printhead. Thus, the printhead prints parallel lines on the top surface. For printing a plurality of objects, several printheads for the same color have to be arranged in series. In order to achieve gapless printing, such rows of printheads are arranged offset from each other in such a way that the last print nozzle of one printhead is located directly behind or next to the first nozzle of the following printhead at the same distance from each other as the nozzles of each printhead. This setting up, also called stitching, of such arrays is very complicated, tedious and error-prone. In addition, each additional printhead requires an additional ink supply, control electronics and other peripheral installations.

SUMMARY OF THE INVENTION

It is an object of the present invention to enable printing on the top surface of three- dimensional objects. In particular, it is an object of the present invention to enable printing on both a lateral surface and a top surface of cylindrical objects. Further, it is an object of the present invention to enable printing on the top and lateral surface of cylindrical objects at an elevated throughput with increased reliability and a minimum number of printheads.

The above object is solved by a method for printing on a top surface of three- dimensional objects according to claim 1 and a printing system according to claim 10. Preferred embodiments are set forth in the present specification, the figures as well as the dependent claims. Specifically, the present invention provides a method for printing on a top surface of three-dimensional objects, particularly screw caps, the method comprising the steps of arranging a plurality of three-dimensional objects in a circumferential direction about a center axis on corresponding mandrels for receiving a three-dimensional object, such that the top surface of each three-dimensional object lies on a reference plane which is perpendicular to the center axis; subsequently passing the three-dimensional objects underneath a printhead by a rotational movement of the plurality of three-dimensional objects about the center axis; and subsequently printing the top surface of each three-dimensional object while it passes underneath the printhead.

That is, the three-dimensional object to be printed is moved in the rotational movement coming from one side with respect to the printhead, passes the printhead underneath, and is further moved in the rotational movement away from the printhead. By keeping the rotational movement, the next three-dimensional object is analogously moved towards, underneath and away from the printhead.

Thus, as all objects to be printed are subsequently passed underneath said printhead, only one printhead is necessary for printing on all three-dimensional objects.

Within the context of this application, the term“screw cap” is to be understood to also comprise shells, a production precursor of ready to use screw caps. Screw caps comprise rollon caps, as well as caps with a preformed internal thread.

If it is desired to print on the top surface with several colors, analogously, only one printhead per color is needed. Preferably, the plurality of printheads is arranged in a circumferential direction with respect to the center axis such that by rotational movement of the three-dimensional objects, the three-dimensional objects subsequently pass each of the plurality of printheads. That is, a radius on which the plurality of three-dimensional objects is arranged with respect to the center axis preferably is similar or equal to a radius on which the plurality of printheads is arranged.

In addition, the setup of a system configured for performing the method according to claim 1 is significantly easier than stitching of the ordinary system which is configured for translating the top surfaces in a linear movement underneath the printheads according to prior art.

By the above described method, it is further possible to significantly reduce the complexity of the system, as the method according to claim 1 can be performed with a significantly smaller total amount of printheads, in particular compared to translating the top surfaces in a linear movement underneath the printheads, depending on the diameter of the rotating system 50 % or even much more of the printheads can be omitted.

In addition to omitting printheads, also the relating additional ink supply, control electronics and other peripheral installations can be omitted.

Preferably, the printhead is held in a position with a fixed distance with respect to the center axis at least during the rotational movement.

The printhead preferably comprises a size, in particular a length, such that it covers total width of the top surface in the radial direction with respect to the center axis which passes underneath the printhead.

According to another preferred embodiment, the method comprises rotating the three- dimensional object to be printed in a counter rotating sense with respect to the rotational movement about a mandrel axis of the mandrel while it passes the printhead.

Thereby, it is possible to compensate an angular distortion caused by the rotational movement of the three-dimensional object about the center axis during printing. With other words, by the rotational movement of the three-dimensional objects underneath the printhead, a geometric distortion of the printed image on the top surface is created with respect to an original graphic intended to be printed, as the speed of a point on the top surface increases proportionally to the radius of said point with respect to the center axis. Thus, a center-to- center distance between two adjacent dots printed by the printhead increases with increasing radius with respect to the center axis. That is, for example a square as graphic to be printed onto the top surface would result in an substantially isosceles trapezoid after printing on the top surface, wherein the smaller one of the parallel sides is oriented towards the center axis and the longer one of the parallel sides of the trapezoid is oriented away from the center axis. Thus, the side legs of the trapezoid comprise a certain angle with respect to a radial direction from the center axis. This angular distortion, hence, can be compensated by the counter rotation of the three-dimensional object about the mandrel axis of the mandrel on which a three-dimensional object is placed.

Moreover, due to the increasing distance of adjacent dots printed by the printheads with increasing radius from the center axis of the rotational movement, a color intensity decreases with increasing radius with respect to the center axis. This leads to a color intensity gradient in the printed image with respect to the original graphic. By the counter rotation of the three-dimensional object about the mandrel axis, also the color intensity gradient can be compensated. Thus, the color intensity of the original graphic and of the printed image is similar or even substantially equal.

According to another preferred embodiment, an absolute value of a rotational speed of the rotational movement is equal to an absolute value of a rotational speed of the rotation of the mandrel. Thereby, the angular distortion can substantially completely be compensated such that, referring to the above example concerning the square, both side legs of the image are aligned substantially parallel to the radial direction, and hence oriented equally to those of the original graphic.

The rotational movement of the three-dimensional object underneath the printhead also results in a radial distortion of the graphic when printed onto the top surface. Referring to the above described example of the square which results in the trapezoid, both parallel sides of the trapezoid thus comprise the shape of an arc having its center oriented towards the center axis. With other words, the smaller one of the parallel sides comprises a concave shape with respect to the trapezoid, and the longer one of the parallel sides comprises a convex shape with respect to the trapezoid. For compensating this sort of distortion, according to another preferred embodiment a graphic to be applied onto the top surface is distorted in a compensation step prior to printing the top surface, wherein the distorted graphic is printed on the top surface. With other words, in the compensation step, the graphic to be printed onto the top surface is distorted contrary to the radial distortion described above, such that the radial distortion can be minimized or even fully compensated.

According to another preferred embodiment, the compensating step of distorting the graphic contains:

Dividing the graphic into rows to be distorted;

Defining a symmetry axis of the graphic to be distorted, wherein the symmetry axis is aligned parallel to the rows;

Starting from a first end of the graphic with respect to the symmetry axis, shifting each row by an predetermined incremental amount with respect to its antecedent row in a distortion direction until the symmetry axis is reached, and shifting each following row by the predetermined incremental amount with respect to its antecedent row in a direction contrary to the distortion direction.

Thereby, the compensation can easily be implemented and applied to graphics of all shape. Furthermore, such a compensation and distortion, respectively, is quite robust. Hence, it is possible to significantly reduce or even totally compensates a distortion of the image to be printed caused by printing in a rotational movement with a combined mechanical and image processing method.

Preferably, the incremental amount is adjusted to the size of the graphic to be printed and/or to the geometry of the system, in particular to the distance of the center axis to the printhead.

According to another preferred embodiment, each row comprises a line width according to a pixel of the graphic to be distorted.

According to yet another preferred embodiment, the incremental amount is determined according to a width of a pixel of the graphic to be distorted.

According to another preferred embodiment, the compensation step is performed based on an algorithmic compensation.

When the method further comprises printing on a lateral surface of the three- dimensional objects, wherein between the step of printing on the top-surfaces and the step of printing on the lateral surfaces, the arrangement of the plurality of three-dimensional objects is tilted such that a least a part of the lateral surface of a three-dimensional object is tangential to the reference plane, according to another preferred embodiment, it is also possible to print on the lateral surface of the three-dimensional objects, and thus, nearly all surfaces facing radially outwards with respect to the center of the three-dimensional object can be printed.

The method is particularly beneficial when, according to another preferred embodiment, the three-dimensional object comprises a circular top surface and/or wherein the three-dimensional object is a substantially cylindrical object.

As already mentioned above, the above object is furthermore solved by a printing system according to claim 10.

Accordingly, a printing system for three-dimensional objects, particularly screw caps, is provided, comprising a mounting device having a plurality of mandrels for receiving a three-dimensional object in a circumferential direction around a center axis, a printhead that is configured to print on surfaces of the three-dimensional objects in a reference plain, wherein the plurality of mandrels is rotatable about the center axis, wherein the system is configured to perform the method of any one of the preceding claims.

By the printing system, the advantages and affects described with regard to the method above are reached analogously. A mounting device, a mandrel and a printhead as well as their arrangement to each other in a printing system are basically known from PCT/US2018/022948, the content of which is herewith incorporated by reference in its entirety.

According to a preferred embodiment, each mandrel comprises a mandrel axis, wherein each mandrel is rotatable about its mandrel axis. Thereby, the mandrels which are configured to hold the three-dimensional objects to be printed on can be rotated. Preferably, the mandrels are configured such that all mandrels can be rotated simultaneously, or the mandrels are configured such that at least one of the mandrels can be rotated independently, wherein preferably all mandrels are rotatable independently from each other.

According to another preferred embodiment, the printing system further comprises a compensation device configured to perform a compensation of a graphic to be applied onto the top surface of the three-dimensional objects according to any one of above described embodiments. Thereby, the conversation step described above can be performed by the printing system, such that it is not necessary to prepare or preprocess the graphic to be printed before delivering it to the printing system.

Alternatively, the compensation step could be performed separately to the printing system, and the distorted graphic is delivered to the printing system.

A very simple and reliable structure of the printing system is achieved, when the compensation device is integrated in a system control for controlling the printing system.

[0042] According to another preferred embodiment, the compensation device comprises a CPU.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and further features and advantages of the invention will become more readily apparent from the following detailed description of preferred embodiments of the invention with reference to the accompanying drawings, in which reference signs designate features, and in which:

Fig. 1 schematically shows a top view of a printing system according to a first embodiment of the present invention;

Fig. 2 schematically shows a perspective side view of a mounting device of the printing system from Figure 1 ; Fig. 3 schematically shows the printing system of Figure 1 and a speed distribution according to a rotational movement about a center axis;

Fig. 4 schematically shows a center-to-center distance of dots printed by a printhead of the printing system onto a top surface of a three-dimensional object;

Fig. 5A schematically shows a graphic to be printed onto the top surface;

Fig. 5B schematically shows the graphic of Figure 5A printed on a top surface of a three-dimensional object which passed the printhead in a rotational movement;

Fig. 6A and 6B schematically show a color intensity gradient of the image shown in Figure 5B with respect to the original graphic shown in Figure 5A;

Fig. 7 schematically shows a detailed view of the printing system according to Figure 1 , wherein a speed distribution caused by a rotation of the mandrel about its mandrel axis is depicted;

Figure 8 schematically shows a resulting speed distribution caused by superposition of the speed distribution caused by the rotational movement according to Figure 3 and the speed distribution caused by the rotation about the mandrel axis;

Fig. 9A-9C show an original image of the graphic to be printed (9A), a resulting image (9B) caused by printing on a top surface of a three-dimensional object which passed the printheads in a rotational movement, and a resulting image (9C) caused by printing on a top surface of a three-dimensional object which passed the printheads in a rotational movement and a counter rotation of the three-dimensional object about the mandrel axis;

Fig. 10 A- 10C show the color intensity of the images of figures 9A-9C;

Figure 11 A shows an original image of the graphic to be printed;

Figure 1 1 B shows the image of Figure 1 1 A distorted by a compensation step prior to printing;

Figure 12 shows a resulting image caused by printing the image of Figure 1 IB on a top surface of a three-dimensional object which passed the printheads in a rotational movement and a rotation of the three-dimensional object about the mandrel axis;

Figure 13 schematically shows a graphic to be printed, divided into parallel rows; Figure 14 schematically shows the graphic of Figure 13 after being distorted in a compensation step prior to printing;

Figure 15 schematically shows another graphic being distorted in a compensation step prior to printing;

Figure 16A shows another graphic to be printed; and Figure 16B shows the graphic of Figure 16A after being distorted in a compensation step prior to printing.

DETAILED DESCRIPTION OF THE INVENTION

Figure 1 schematically shows a top view of a printing system 1 according to a first embodiment of the present invention. The printing system 1 comprises a mounting device 2 which has a plurality of mandrels 20 arranged in a circumferential direction about a center axis 5. The mounting device 2 can be rotated about the center axis 5, and thus, the mandrels 20 can be rotated about the center axis 5.

Each mandrel 20 comprises a mandrel axis 22, wherein each mandrel 20 is rotatable about its mandrel axis 22. The printing system 1 further comprises a printhead 4. The printhead 4 is configured to print on surfaces in a reference plane (not shown). The mandrels 20 are further configured for receiving a three-dimensional object 3 such that a top surface 30 of the three-dimensional object 3 is arranged in the reference plane. The printhead 4 is arranged with respect to the center axis 5 such that it is able to print the top surface 30 of a three-dimensional object 3 when it is rotated underneath the printhead 4.

Figure 2 schematically shows a perspective side view of a mounting device 2 of the printing system 1 from figure 1. As can be clearly seen from figure 2, the mandrels 20 hold the three-dimensional objects 3 such that the top surface 30 of the plurality of three- dimensional objects 3 are each held in the same height with respect to the center axis 5, thus all top surfaces 30 are laying in the same plane, the reference plane.

In the present embodiment, the mounting device 2 comprises 6 mandrels 20. Alternatively, the mounting device 2, of course, may comprise a different amount of mandrels 20, preferably 12, 16, 20, 24 or 26. The mounting device 2 may also comprise any other amount of mandrels 20.

For printing on the top surface 30 of a three-dimensional object 3, the following steps are performed on the printing system 1 according to figures 1 and 2. After arranging the plurality of three-dimensional objects 3 in the circumferential direction about the center axis 5 on the mandrels 20 such that the top surface 30 of each three-dimensional object 3 lies in the reference plane as described above, the three-dimensional objects 3 are subsequently passed underneath the printhead 4 by the rotational movement in the rotational movement direction 50 about the center axis 5. In this way, all the top surfaces 30 can be printed with the printhead 4. When a top surface 30 passes the printhead 4, the printhead prints onto said top surface 30. Hence, the top surface 30 of each three-dimensional object 3 can subsequently printed by this one printhead 4.

If it is desired to print graphics comprising several colors onto the top surfaces 30, optionally, printing system 1 can comprise a plurality of printheads 4, wherein each printhead 4 is configured to print in a certain color. Preferably, the plurality of printheads 4 is also arranged in a circumferential direction with respect to the center axis 5.

Figure 3 schematically shows the printing system 1 of figure 1 and a speed distribution of several points on the top surface 30 due to a rotational movement of the mandrels 20 about the center axis 5. By reference sign 50, the direction of the rotational movement of the mandrels 20 about the center axis 5 is indicated. With increasing radius with respect to the center axis 5, the speed increases. That is, and inner point 33 of the top surface 30 rotating on an inner diameter 52 with respect to the center axis 5 comprises a speed v, a middle point 34 of the top surface 30 rotating on a middle diameter 53 comprises an accordingly increased speed v’, and an outer point 35 of the top surface 30 rotating about an outer diameter 54 comprises a further increased speed v”. Thus, the rotational movement about the center axis 5 results in a velocity gradient of pointing radially outwards with respect to the center axis 5.

Turning to Figure 4, a resulting center-to-center distance of dots 6 printed by the printhead 4 of the printing system 1 onto the top surface 30 of a three-dimensional object 3 rotationally moved about the center axis 5 is shown. As can be clearly seen, dots 6 printed by the printhead 4 in the inner diameter 52 comprise a small center-to-center distance, as the speed v in the inner diameter 52 is quite small. In turn, dots 6 printed by the printhead 4 in the middle diameter 53 comprise a middle center-to-center distance bigger than the center-to- center distance of the dots 6 in the inner diameter 52, as the speed v’ is greater than the speed v. Accordingly, dots 6 printed by the printhead 4 on the outer diameter 54 comprise a big center-to-center distance compared to the dots 6 printed in the inner diameter 52 and a middle diameter 53, when the nozzles of the printhead 4 open and close periodically.

The aforementioned leads to an angular distortion of an image printed onto the top surface 30 with respect to its original graphic form, as is further illustrated with respect to Figures 5A and 5B.

In this regard, Figure 5A schematically shows a graphic 7 to be printed onto the top surface 30. The graphic 7 according to this example is a square comprising side legs 70 and, with respect a radial direction 56 with respect to the center axis 5, further comprises an inner side 71 and an outer side 72.

Figure 5B schematically shows the resulting image 8 of the graphic 7 of Figure 5A which was printed on the top surface 30 of a three-dimensional object 3. As can be clearly seen in comparison with the original graphic 7, image 8 comprises an angular distortion. That is, the side legs 80 are oriented in an angle 84 with respect to the original orientation of the side legs 70. Thus, the image 8 printed onto the top surface 30 does not comprise the form of the square as the original graphic 7, but comprises the form of a substantially isosceles trapezoid, wherein the inner side 81 is the smaller one of the parallel sides and the outer side 82 is the longer one of the parallel sides of the trapezoid.

In addition, the inner side 81 and the other side 82 of image 8 comprise the shape of an arc having its center oriented towards the center axis 5. With other words, the inner side 81 comprises a concave shape with respect to the trapezoid, and the outer side 82 comprises a convex shape with respect to the trapezoid. Hence, the rotational movement of the three- dimensional object 3 underneath the printhead 4 also results in a radial distortion of the graphic 7 when printed onto the top surface 30.

Moreover, due to the above described radial velocity gradient, and thus due to the increasing distance of adjacent dots 6 printed by the printhead 4 with increasing radius from the center axis 5, a color intensity of the image 8 decreases with increasing radius with respect to the center axis 5 compared to the original graphic 7. The resulting intensity gradient is depicted via reference sign 86 in figure 5B. The intensity gradient 86, showing the decreasing color intensity, is parallel to the radial direction 56.

In Figures 6A and 6B, the color intensity gradient of the image 8 shown in Figure 5B is shown with respect to the original graphic 7 shown in Figure 5A in greyscale.

In order to compensate the radial distortion, the three-dimensional object 3 is rotated in a counter rotating sense with respect to the rotational movement 50 about the mandrel axis 22 of the mandrel 20 while it passes the printhead 4.

Figure 7 schematically shows a detailed view of the printing system 1 according to figure 1, wherein a speed distribution caused by a rotation of the mandrel 20 about its mandrel axis 22 alone is depicted. As can be seen, the rotation direction 24 is oriented contrary to the rotational movement direction 50.

The rotation about the mandrel axis 20 causes a speed distribution directly proportional to the radius with respect to the mandrel axis 22. Hence, as the mandrel axis 22 is located on the middle diameter 53, at the middle point 34, no speed is generated via the rotation about the mandrel axis 22. The inner point 33 and the outer point 35 each comprise a mandrel speed v _m .

Figure 8 schematically shows a resulting speed distribution caused by superposition of the speed distribution by means of the rotational movement 50 according to figure 3 and the speed distribution by means of the rotation 24 about the mandrel axis 22.

At the inner point 33, speed v and mandrel speed v _m comprise the same sense of direction, thus they sum up to a resulting speed VR. At the middle point 34, speed v’ is the resulting speed VR’. At the outer point 35, the speed v” comprises a sense of direction opposing to the sense of direction of the mandrel speed v _m . Thus, the resulting speed VR” at outer point 35 is speed v” subtracted by mandrel speed v _m .

In this embodiment, an absolute value of a rotational speed of the rotational movement 50 is equal to an absolute value of a rotational speed of the rotation 24 about the mandrel axis 22. Hence, the resulting speeds VR, V _r ’ and VR” at inner point 33, middle point 34 and outer point 35 are equal.

Figure 9A again shows the original graphic 7 to be printed, Figure 9B shows a resulting image 8 caused by printing on the top surface 30 of a three-dimensional object 3 which passed the printhead 4 in a rotational movement 50 only, and Figure 9C shows a resulting image 8 caused by printing on the top surface 30 of a three-dimensional object 3 which passed the printhead 4 in a rotational movement 50, wherein simultaneously, the three- dimensional object 3 was rotated in the rotation direction 24 about the mandrel axis 22.

As can be clearly seen from figures 9A-9C, in particular by comparison of graphic 7 shown in Figure 9A with image 8 shown in figure 9C, the angular distortion of the side legs 80 can be compensated by the rotation about the mandrel axis 22.

In addition, by the counter rotation about the mandrel axis 22, the color intensity gradient described with respect to figures 5 A and 5B and 6A and 6B, is compensated. Hence, there is no difference in color intensity between the graphic 7 and the image 8 shown in Figure 9C.

For better understanding, Figures 10 A- 10C show the color intensity of the images of Figures 9A-9C in grayscale.

As can be seen by synopsis of the above figures, by performing the rotational movement 50 together with the rotation about the mandrel axis 22, the angular distortion can be compensated. By superposition of the rotational movement about the center axis 5 and the rotation about the mandrel axis 22, a radial distortion is caused having a contrary effect as a radial distortion caused by the rotational movement alone. Thus, as can be seen in figure 9C, the inner side 81 and the outer side 82 comprise a form of an arc having its center oriented away from the center axis 5. For its compensation, prior to printing, the graphic 7 is distorted in a compensation step, wherein the such distorted graphic is afterwards printed on the top surface.

Figure 11 A shows the original image 7 of the graphic to be printed according to figure 5A. Figure 1 IB shows a distorted graphic 9 based on graphic 7 after being distorted by the above mentioned compensation. As can be seen, the inner side 96, which corresponds to the inner side 71, and outer side 68, which corresponds to the outer side 72 are each distorted to comprise to form of an arc having its center oriented towards the center axis 5.

When the such distorted graphic 9 is printed onto the top surface 30, wherein the three-dimensional object 3 is passed underneath the printhead 4 in the rotational movement about the center axis 5 in the rotational movement direction 50, and simultaneously, the three-dimensional object 3 is rotated about the mandrel axis 22 in the rotation direction 24, the result is an image 8 as shown in figure 12, wherein image 8 substantially comprise the shape of the original graphic 7 as shown in figure 5 A and 11 A, respectively.

With respect to figures 13 to 15, an exemplary embodiment of a distortion performed in the compensation step is described.

Figure 13 schematically shows the graphic 7 to be printed, which has been divided into parallel rows 90. In addition, a symmetry axis 92 of the graphic 7 has been defined, wherein the symmetry axis 92 is aligned parallel to the rows 90. Here, each row 90 comprises a line width according to a pixel size of a pixel 94 of the graphic 7. Alternatively, the rows 90 can be determined to have any other suitable width.

Figure 14 schematically shows the distorted graphic 9 based on the graphic 7 of figure 13 after being distorted by means of the compensation step. Starting from a first end of the graphic with respect to the symmetry axis, here the upper end with respect to the orientation of the graphic in figures 13 and 14, each row 90 was shifted by an predetermined incremental amount with respect to its antecedent row 90 in a distortion direction 95 which is parallel to the symmetry axis 92 until the symmetry axis 92 is reached, all subsequent rows 90 were each shifted by the predetermined incremental amount with respect to its antecedent row 90 in a direction contrary to the distortion direction 95, resulting in the distorted graphic as shown in figure 14. Here, the incremental amount is determined according to a width of the pixels 94 of the graphic 7. Thus, each row 90 is displaced in the distortion direction 95 about the width of a pixel 94 with respect to an antecedent row 90.

Alternatively, the incremental amount may be predetermined to any other suitable length.

Figure 15 schematically shows another graphic 9 based on the graphic 7 after being distorted in a compensation step, wherein here, the division into rows resulted in an uneven total amount of rows 90.

Figure 16A shows another graphic 7 to be printed, and Figure 16B shows the graphic 7 of Figure 16A after being distorted in a compensation step prior to printing, resulting in distorted graphic 9.

For performing the compensation step, the printing system I comprises a compensation device (not shown) configured to perform the compensation step of the graphic 7 to be applied onto the top surface 30 of the three-dimensional objects 3 as described above. The compensation device is further configured to perform the compensation step based on an algorithm, wherein the algorithm is integrated in a computer implemented method which is performed via a CPU of the compensation device in form of a computer program.

It will be obvious for a person skilled in the art that these embodiments and items only depict examples of a plurality of possibilities. Hence, the embodiments shown here should not be understood to form a limitation of these features and configurations. Any possible combination and configuration of the described features can be chosen according to the scope of the invention.

Reference Si tin List

1 printing system

2 mounting device

20 mandrel

22 mandrel axis

24 rotation direction

3 three-dimensional object

30 top surface

32 lateral surface

33 inner point

34 middle point

35 outer point

4 printhead

5 center axis

50 rotational movement direction

52 inner diameter

53 middle diameter

54 outer diameter

56 radial direction

6 dot

7 graphic

70 side leg

71 inner side

72 outer side

8 image

80 side leg

81 inner side

82 outer side

84 angle

86 intensity gradient

9 distorted graphic

90 row

92 symmetry axis 94 pixel

95 distortion direction

96 inner side

98 outer side v, v\ v” speed

V _m mandrel speed VR, V _r \ VR” resulting speed